MOTION OF A PARTICLE
108. E. Atwood's Machine. — The problem is to find the equations of motion of two particles connected by means of a string of negligible mass which is slung over a smooth pulley.
Let mi and m2 be the masses of the particles. Then considering each particle separately we obtain the following for the force equations:
where T is the tensile force in the string. Eliminating T between equations (a) and (b) we obtain
dv (mi + m*) — = (mi - w2) g, (c)
dt dv dt
Therefore the acceleration is constant and consequently the equations of motion are obtained by substituting this value of the acceleration in equations (1) to (3) of page 113:
Eliminating -7- between equations (a) and (b) we have